This paper reports a study concerned with the selection of mathematically talented students at the beginning of secondary school in Australia using a version of the College Board's Scholastic Aptitude Test (SAT). Some young students achieved scores comparable with older mathematically able students and with college-bound students in USA. Teacher nomination of students as talented resulted in the selection of considerably different groups of students to those selected using the SAT. Marked sex differences, in favour of boys, are noted and discussed. Three different procedures for comparing item responses of younger and older groups are employed, leading to the conclusion that younger and older students respond to SAT items in qualitatively different ways. Comparison procedures based on the Rasch model for measurement are favoured.